Rational

Rational Numbers extension to SuperCollider.

Install

Quarks.install("https://github.com/smoge/Rational")

Quick Start

Rational(6, 4)           // -> 3 %/ 2
Rational("8/4")          // -> 2 %/ 1
Rational(0.33333)        // -> 1 %/ 3
5 %/ 7 == Rational(5, 7) // -> true

Basic arithmetic stays in rational form:

a = Rational(3, 2);
b = 4 %/ 5;
a + b;       // -> 23 %/ 10
a - b;       // -> 7 %/ 10
a * b;       // -> 6 %/ 5
a / b;       // -> 15 %/ 8
a.pow(2);    // -> 9 %/ 4

Rationals compare and sort alongside other numbers:

(7 %/ 3) > (2 %/ 1) // -> true
[1, 1.5, 3 %/ 5, 8 %/ 5, 1.342].sort;

Convert when needed:

(5 %/ 7).asFloat   // -> 0.71428571428571
pi.asRational(999) // -> 355 %/ 113

Operations with exact rational answers return Rational values:

(7 %/ 2).floor       // -> 3 %/ 1
(1 %/ 3).frac        // -> 1 %/ 3
(1 %/ 3).mod(1 %/ 7) // -> 1 %/ 21

Other Number methods use asFloat when no rational answer exists. respondsTo reports those forwarded methods:

(1 %/ 3).sqrt              // -> 0.57735026918963
(1 %/ 2).respondsTo(\sqrt) // -> true

Zero denominators, division by zero, reciprocal of zero, and terms that are not numbers throw Error.

Precision Notes

Rational stores numerator and denominator as 64 bit Floats. This avoids SuperCollider Integer wrapping during rational arithmetic.

SuperCollider still wraps large integer literals before Rational sees them. If you need a term outside the 32 bit Integer range, write it with .0.

Arithmetic cancels common factors before multiplying where possible. This keeps many intermediate values smaller and preserves more precision, but it does not make the numeric range unlimited.

Tests

TestRational.run

The test suite covers construction, arithmetic, comparison, sorting, Float storage, large value precision, zero denominators, inf, NaN, string parsing, and deterministic randomized algebra.

More Examples

See the SCDoc help in your IDE. Source: HelpSource/Rational.schelp.